Abstract

Przemski introduced D(?, s)-set, D(?, b)-set, D(p, sp)-set, D(p, b)- set and D(b, sp)-set to obtain several decompositions of continuity. In this paper, we extend these sets via bioperation and obtain new decompositions of continuity.

Highlights

  • Generalized open sets play a very important role in General Topology and they are the research topics of many topologists worldwide

  • Kasahara [1] defined the concept of an operation on topological spaces

  • Przemski in [5], analyze some forms of decomposition of continuous and α-continuous using D(α, s)-set, D(α, b)-set, D(p, sp)-set, D(p, b)-set and D(b, sp)-set In this paper, we introduce some new types of sets via bioperation and obtain some theorems related with decomposition of continuity

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Summary

Introduction

Generalized open sets play a very important role in General Topology and they are the research topics of many topologists worldwide. A significant theme in General Topology and Real analysis concerns the various modified forms of continuity, separation axioms etc. Kasahara [1] defined the concept of an operation on topological spaces. Ogata and Maki [4] introduced and studied the notion of τγ∨γ0 which is the collection of all γ ∨ γ0-open sets in a topological space (X, τ ). Przemski in [5], analyze some forms of decomposition of continuous and α-continuous using D(α, s)-set, D(α, b)-set, D(p, sp)-set, D(p, b)-set and D(b, sp)-set In this paper, we introduce some new types of sets via bioperation and obtain some theorems related with decomposition of continuity

Preiliminaries
Some subsets in topological spaces
Some decomposition theorems

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